Related Experiment Video
Updated: Mar 2, 2026
10:23
Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
Published on: December 1, 2023
1.1K
SU-E-T-08: Simple Governing Equations for Tumor Growth.
1University of Minnesota, Minneapolis, MN.
Medical Physics
|May 19, 2017
Summary
This study models tumor growth using differential equations, revealing that limited blood supply, not just cell proliferation, causes growth saturation. These findings explain the Gompertz equation and tumor growth dynamics.
Area of Science:
- Mathematical Biology
- Oncology
- Biophysics
Background:
- Tumor microenvironment significantly impacts cancer cell proliferation and growth dynamics.
- Understanding the relationship between nutrient supply and tumor expansion is crucial for developing effective cancer therapies.
Purpose of the Study:
- To derive simplified differential equations modeling tumor temporal growth.
- To incorporate the effects of the tumor microenvironment, specifically nutrient availability, on cell proliferation.
Main Methods:
- Modeled cause-effect relationships between cell proliferation and blood-borne nutrients (oxygen, glucose).
- Formulated and simplified rate equations to obtain two differential equations.
- Numerically solved equations, varying a parameter representing relative blood volume growth rate.
Main Results:
- Tumor volume increases exponentially when blood volume matches tumor growth.
- Tumor growth saturates (1000-fold increase) when blood volume lags behind tumor expansion.
- Tumor growth ceases with complete cessation of blood supply (kappa=0).
Conclusions:
- Derived differential equations accurately reproduce tumor growth patterns, including Gompertzian kinetics.
- Relative lack of blood supply explains tumor growth saturation in larger tumors by decreasing proliferation rates.
- Future models will incorporate the effects of radiation therapy on tumor growth.
Related Concept Videos
02:33Exponential Equations for Modeling Growth
284
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
284
01:25Modeling with Differential Equations
131
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
131
02:53Adaptive Mechanisms in Cancer Cells
7.2K
Cancer cells accumulate genetic changes at an abnormally rapid rate due to the defects in the DNA repair mechanisms. From an evolutionary perspective, such genetic instability is advantageous for cancer development. Mutant cell lines accumulate a series of beneficial mutations that contribute to their progression into cancer.
Some of the advantages that cancer cells have on normal cells include - enhanced ability to divide without terminally differentiating, induce new blood vessel formation,...
Some of the advantages that cancer cells have on normal cells include - enhanced ability to divide without terminally differentiating, induce new blood vessel formation,...
7.2K
02:18Cancer
55.1K
Cancers arise due to mutations in genes involved in the regulation of cell division, which leads to unrestricted cell proliferation. Modern science and medicine have made great strides in the understanding and treatment of cancer, including eradicating cancer in some patients. However, there is still no cure for cancer. This is largely due to the fact that cancer is a large group of many diseases.
55.1K
02:07Tumor Progression
7.6K
Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
7.6K
01:27Growth Models with Integration: Problem Solving
82
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
82